The Students had taken an early lead through Ryan Chapman.
However, Dikwena levelled on the stroke of half-time through Mogakolodi Ngele, before the Botswana international converted the winning penalty in the second half.
The match sprung into action in only the second minute when Enocent Mkhabela had a close-range header saved by Wits keeper Emille Baron after Thuso Phala had done well to send a pin-point cross in from the right.
The home side then took the lead on 21 minutes, with Sibusiso Vilakazi playing a pin-point pass to find Chapman, who chipped over Stars goalie Siyabonga Mpontshane.
Wits could have taken a two-goal lead into the interval when they were awarded a penalty after defender Tshepo Gumede fouled Vilakazi in the 35th minute, but the same player saw his effort saved by Mpontshane.
The Clever Boys were made to pay for that miss as Stars equalised a minute before halftime through Ngele. Dikwena striker Henrico Botes laid the ball to the Botswana international, who powered a low shot that beat Baron.
Then, on 60 minutes, Wits’ Sandile Sibande handled in the box, and Ngele made no mistake as he coolly finished from the spot.